Image-forming MR methods which utilize the interaction between magnetic fields and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for imaging of soft tissue they are superior to other imaging methods in many respects, do not require ionizing radiation and are usually not invasive.
According to the MR method in general, the object, for example the body of the patient to be examined, is arranged in a strong, uniform magnetic field whose direction at the same time defines an axis (normally the z-axis) of the co-ordinate system on which the measurement is based. The magnetic field produces different energy levels for the individual nuclear spins in dependence on the magnetic field strength which can be excited (spin resonance) by application of an electromagnetic alternating field (RF field) of defined frequency (so-called Larmor frequency, or MR frequency). From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate frequency (RF pulse), so that the magnetization performs a precessional motion about the z-axis. The precessional motion describes a surface of a cone whose angle of aperture is referred to as flip angle. The magnitude of the flip angle is dependent on the strength and the duration of the applied electromagnetic pulse. In the case of a so-called 90° pulse, the spins are deflected from the z axis to the transverse plane (flip angle 90°).
After termination of the RF pulse, the magnetization relaxes back to the original state of equilibrium, in which the magnetization in the z direction is built up again with a first time constant T1 (spin lattice or longitudinal relaxation time), and the magnetization in the direction perpendicular to the z direction relaxes with a second time constant T2 (spin-spin or transverse relaxation time). The variation of the magnetization can be detected by means of receiving RF coils which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicular to the z-axis. The decay of the transverse magnetization is accompanied, after application of, for example, a 90° pulse, by a transition of the nuclear spins (induced by local magnetic field inhomogeneities) from an ordered state with the same phase to a state in which all phase angles are uniformly distributed (dephasing). The dephasing can be compensated by means of a refocusing pulse (for example a 180° pulse). This produces an echo signal (spin echo) in the receiving coils.
To realize spatial resolution in the body, constant magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving coils then contains components of different frequencies which can be associated with different locations in the body. The signal data obtained via the receiving coils corresponds to the spatial frequency domain and is called k-space data. The k-space data usually includes multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of k-space data is converted to a MR image by means of an image reconstruction algorithm.
In the known so-called three-dimensional (3D) stack-of-stars acquisition scheme (see, e.g., WO 2013/159044 A1), a number of spatially non-selective or slab-selective RF excitations is applied, each followed by the acquisition of one or more MR signals (e.g. gradient echo signals), wherein each MR signal represents a k-space profile. The MR signals are acquired as radial k-space profiles from a number of parallel slices. The slices are arranged at different positions along a slice direction. In the slice direction (e.g. the kz-direction) standard Cartesian phase-encoding is performed, while the MR signals are acquired within each single slice along radial “spokes” that are rotated around the center (kx=ky=0). This results in a cylindrical k-space coverage composed of stacked discs (“stack-of-stars”). Technically, this is realized by generating magnetic field gradients in the in-plane directions of the slices simultaneously and modulating their amplitudes. Different schemes can be used for selecting the temporal order of the k-space profile acquisition steps. E.g., all phase-encoding steps along the slice direction can be acquired sequentially before k-space profiles at different angular positions are acquired. This ensures that periods of Cartesian sampling are kept short, which leads to high data consistency within the stack of slices and preserves the general motion-robustness of radial sampling for the stack-of-stars approach. The Cartesian phase-encoding steps may be performed from the center slice to the k-space periphery (centric out), or in linear order from −kz,max to +kz,max. For the angular ordering, the imaging sequence can use either equidistant angular sampling with multiple interleaves or the so-called golden angle-scheme. In the equidistant scheme, the angular distance is calculated according to ΔΦ=180°/ntotal where ntotal is the total number of spokes. It may be beneficial to acquire the spokes using multiple interleaves (or “rotations”) because the interleaving reduces temporal coherences in k-space. Thus, motion inconsistencies are spread out in k-space and artifacts are attenuated. In the golden angle-scheme, the angle of the k-space profile is incremented each time by ΔΦ=111.25°, which corresponds to 180° multiplied by the golden ratio. Therefore, subsequently sampled spokes always add complementary information while filling the largest gaps within the previously sampled set of spokes. As a consequence, any sequential set of acquired spokes covers k-space approximately uniformly, which enables reconstruction of temporal sub-frames and makes the golden-angle scheme well-suited for dynamic imaging studies.
The afore-described 3D radial stack-of-stars scheme offers several promising advantages for clinical MR imaging like high motion-robustness, benign aliasing artifacts and a continuous updating of k-space center. However, despite these benefits streaking artifacts are often a problem. A higher required radial sampling density and, thus, longer scan times are the consequence.
The ISMRM-abstract 2007 p. 207 ‘Radial undersampling that is variable in kz’ by D. C. Peters et al. discloses a stack-of-stars sampling approach in k-space. A radial undersampling pattern which varies in the kz-dimension is used, acquiring a greater number of projections for central kz-space.